Arithmetic representations of mapping class groups

arXiv2108.12791MaRDI QIDQ6376259

Eduard Looijenga

Publication date: 29 August 2021

Abstract: Let $S$ be a closed oriented surface and $G$ a finite group of orientation preserving automorphisms of $S$ whose orbit space has genus at least $2$. There is a natural group homomorphism from the $G$-centralizer in $Dif{f}^{+}(S)$ to the $G$-centralizer in $Sp(H_1(S))$. We give a sufficient condition for its image to be a subgroup of finite index and a weaker condition for this to have no finite nonzero orbit (the Putman-Wieland property).

Mathematics Subject Classification ID

Bilinear and Hermitian forms (11E39) Low-dimensional topology of special (e.g., branched) coverings (57M12) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

This page was built for publication: Arithmetic representations of mapping class groups